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Mirrors > Home > ILE Home > Th. List > breq12 | Unicode version |
Description: Equality theorem for a binary relation. (Contributed by NM, 8-Feb-1996.) |
Ref | Expression |
---|---|
breq12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | breq1 3932 | . 2 | |
2 | breq2 3933 | . 2 | |
3 | 1, 2 | sylan9bb 457 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 class class class wbr 3929 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-sn 3533 df-pr 3534 df-op 3536 df-br 3930 |
This theorem is referenced by: breq12i 3938 breq12d 3942 breqan12d 3945 posng 4611 isopolem 5723 poxp 6129 rbropapd 6139 ecopover 6527 ecopoverg 6530 ltdcnq 7205 recexpr 7446 ltresr 7647 reapval 8338 ltxr 9562 xrltnr 9566 xrltnsym 9579 xrlttr 9581 xrltso 9582 xrlttri3 9583 xposdif 9665 exmidsbthrlem 13217 |
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